A Survey on Soft Subspace Clustering

Subspace clustering (SC) is a promising clustering technology to identify clusters based on their associations with subspaces in high dimensional spaces. SC can be classified into hard subspace clustering (HSC) and soft subspace clustering (SSC). While HSC algorithms have been extensively studied and well accepted by the scientific community, SSC algorithms are relatively new but gaining more attention in recent years due to better adaptability. In the paper, a comprehensive survey on existing SSC algorithms and the recent development are presented. The SSC algorithms are classified systematically into three main categories, namely, conventional SSC (CSSC), independent SSC (ISSC) and extended SSC (XSSC). The characteristics of these algorithms are highlighted and the potential future development of SSC is also discussed.Comment: This paper has been published in Information Sciences Journal in 201

Semantic distillation: a method for clustering objects by their contextual specificity

Techniques for data-mining, latent semantic analysis, contextual search of databases, etc. have long ago been developed by computer scientists working on information retrieval (IR). Experimental scientists, from all disciplines, having to analyse large collections of raw experimental data (astronomical, physical, biological, etc.) have developed powerful methods for their statistical analysis and for clustering, categorising, and classifying objects. Finally, physicists have developed a theory of quantum measurement, unifying the logical, algebraic, and probabilistic aspects of queries into a single formalism. The purpose of this paper is twofold: first to show that when formulated at an abstract level, problems from IR, from statistical data analysis, and from physical measurement theories are very similar and hence can profitably be cross-fertilised, and, secondly, to propose a novel method of fuzzy hierarchical clustering, termed \textit{semantic distillation} -- strongly inspired from the theory of quantum measurement --, we developed to analyse raw data coming from various types of experiments on DNA arrays. We illustrate the method by analysing DNA arrays experiments and clustering the genes of the array according to their specificity.Comment: Accepted for publication in Studies in Computational Intelligence, Springer-Verla

DSL: Discriminative Subgraph Learning via Sparse Self-Representation

The goal in network state prediction (NSP) is to classify the global state (label) associated with features embedded in a graph. This graph structure encoding feature relationships is the key distinctive aspect of NSP compared to classical supervised learning. NSP arises in various applications: gene expression samples embedded in a protein-protein interaction (PPI) network, temporal snapshots of infrastructure or sensor networks, and fMRI coherence network samples from multiple subjects to name a few. Instances from these domains are typically ``wide'' (more features than samples), and thus, feature sub-selection is required for robust and generalizable prediction. How to best employ the network structure in order to learn succinct connected subgraphs encompassing the most discriminative features becomes a central challenge in NSP. Prior work employs connected subgraph sampling or graph smoothing within optimization frameworks, resulting in either large variance of quality or weak control over the connectivity of selected subgraphs. In this work we propose an optimization framework for discriminative subgraph learning (DSL) which simultaneously enforces (i) sparsity, (ii) connectivity and (iii) high discriminative power of the resulting subgraphs of features. Our optimization algorithm is a single-step solution for the NSP and the associated feature selection problem. It is rooted in the rich literature on maximal-margin optimization, spectral graph methods and sparse subspace self-representation. DSL simultaneously ensures solution interpretability and superior predictive power (up to 16% improvement in challenging instances compared to baselines), with execution times up to an hour for large instances.Comment: 9 page

Discriminative variable selection for clustering with the sparse Fisher-EM algorithm

The interest in variable selection for clustering has increased recently due to the growing need in clustering high-dimensional data. Variable selection allows in particular to ease both the clustering and the interpretation of the results. Existing approaches have demonstrated the efficiency of variable selection for clustering but turn out to be either very time consuming or not sparse enough in high-dimensional spaces. This work proposes to perform a selection of the discriminative variables by introducing sparsity in the loading matrix of the Fisher-EM algorithm. This clustering method has been recently proposed for the simultaneous visualization and clustering of high-dimensional data. It is based on a latent mixture model which fits the data into a low-dimensional discriminative subspace. Three different approaches are proposed in this work to introduce sparsity in the orientation matrix of the discriminative subspace through $\ell_{1}$-type penalizations. Experimental comparisons with existing approaches on simulated and real-world data sets demonstrate the interest of the proposed methodology. An application to the segmentation of hyperspectral images of the planet Mars is also presented

Penalized Clustering of Large Scale Functional Data with Multiple Covariates

In this article, we propose a penalized clustering method for large scale data with multiple covariates through a functional data approach. In the proposed method, responses and covariates are linked together through nonparametric multivariate functions (fixed effects), which have great flexibility in modeling a variety of function features, such as jump points, branching, and periodicity. Functional ANOVA is employed to further decompose multivariate functions in a reproducing kernel Hilbert space and provide associated notions of main effect and interaction. Parsimonious random effects are used to capture various correlation structures. The mixed-effect models are nested under a general mixture model, in which the heterogeneity of functional data is characterized. We propose a penalized Henderson's likelihood approach for model-fitting and design a rejection-controlled EM algorithm for the estimation. Our method selects smoothing parameters through generalized cross-validation. Furthermore, the Bayesian confidence intervals are used to measure the clustering uncertainty. Simulation studies and real-data examples are presented to investigate the empirical performance of the proposed method. Open-source code is available in the R package MFDA